A helicopter hovers 500 feet above ground, over a large opentank full of liquid (not water). A dense compact object weighing160 pounds is dropped (released from rest) from the helicopter intothe liquid. Assume that air resistance is proportional toinstantaneous velocity v while the object is in the air and thatviscous damping is proportional to v2 after the object has enteredthe liquid. For air take the constant of proportionality to be k =1 /A helicopter hovers 500 feet above ground, over a large opentank full of liquid (not water). A dense compact object weighing160 pounds is dropped (released from rest) from the helicopter intothe liquid. Assume that air resistance is proportional toinstantaneous velocity v while the object is in the air and thatviscous damping is proportional to

v2

after the object has entered the liquid. For air take theconstant of proportionality to be

k =

1

4

,

and for the liquid take it to be

k = 0.1.

Assume that the positive direction is downward. If the(above-ground) tank is 75 feet high, determine the time and theimpact velocity when the object hits the bottom of the tank. [Hint:Think in terms of two distinct IVPs. If you use (13) from Section3.2,

du

a2 − u2

=

1

2a

ln

a + u

a − u

+ c,    |u| ≠ a,

be careful in removing the absolute value sign. You mightcompare the velocity when the object hits the liquid—the initialvelocity for the second problem—with the terminal velocity

vt

of the object falling through the liquid.] (Assume theacceleration due to gravity is

g = 32 ft/s2,

and the mass is m = 160/g. Round your answers to five decimalplaces.)

time     s

velocity     ft/s

4 , and for the liquid take it to be k = 0.1. Assume that thepositive direction is downward. If the (above-ground) tank is 75feet high, determine the time and the impact velocity when theobject hits the bottom of the tank. [Hint: Think in terms of twodistinct IVPs. If you use (13) from Section 3.2,

du a2 − u2 = 1 2a ln a + u a − u + c, |u| ≠ a, be careful inremoving the absolute value sign. You might compare the velocitywhen the object hits the liquid—the initial velocity for the secondproblem—with the terminal velocity vt of the object falling throughthe liquid.] (Assume the acceleration due to gravity is g = 32ft/s2, and the mass is m = 160/g. Round your answers to fivedecimal places.) time s velocity ft/s